Statistical behavior and consistency of classification methods based on convex risk minimization

By Tong Zhang. 2003

935 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Control and Systems Engineering, Optimization & Training

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Citations in the corpus

Quantifying Learning Guarantees for Convex but Inconsistent Surrogates (2018, background): “Consistency of convex surrogates has been the central question of many studies for such problems as binary classification [2, 24, 19], multi-class classification [23, 21, 1, 17], ranking [11, 4, 5, 18, 15] and, more recently, structured prediction [7, 14].”
On Structured Prediction Theory with Calibrated Convex Surrogate Losses (2017, background): “The consistency of convex surrogates is well understood in the case of binary classiﬁcation [46, 4, 39] and there is signiﬁcant progress in the case of multi-class 0-1 loss [45, 42] and general loss functions [2, 35, 44].”
Estimating treatment effect heterogeneity in randomized program evaluation (2013, methodology): “This quantity utilizes the fact that the L2-SVM is an optimal classifier [Lin (2002), Zhang (2004)].”
On the Consistency of Ordinal Regression Methods (2014, result): “Consistency results of this surrogate was proven by Zhang [24].”
Adapting to Unknown Smoothness by Aggregation of Thresholded Wavelet Estimators (2006, neutral): “the Bayes rule f � (x) = Sign(2η(x) − 1), ∀x ∈ X (cf. [ 56 ]).”
Generalization bounds for learning the kernel (2009, background): “As shown in [33, 4], the excess misclassification error usually can be bounded by the excess generalization error:”
Trading convexity for scalability (2006, background): “See ( Zhang, 2004 ) for a general mechanism connecting convex losses to classification error.”
PAC-Bayesian bounds for randomized empirical risk minimizers (2007, methodology): “See Zhang [22] for a complete study of the performance of classiﬁcation methods using these loss functions.”
Oracle inequalities in empirical risk minimization and sparse recovery problems (2011, background): “, McAllester [75], Catoni [31], Audibert [4], Zhang [99, 100, 101] and references therein).”
Multicategory Support Vector Machines, Theory, and Application to the Classiﬁcation of Microarray Data and Satellite Radiance Data (2002, background): “The pairwise approach has the disadvantage of potential variance increase since smaller observations are used to learn each classifier.”
Support Vector Machines with Applications (2006, methodology): “, ZHANG, H. and LEE, Y. (2002). Statistical properties and adaptive tuning of support vector machines. Machine Learning 48 115–136. [42] MARTIN, I., MOGUERZA, J. M. and MUÑOZ, A. (2004). Combining kernel information for support vector classification. Multiple Classifier Systems. Lecture Notes in Com”
Learning the coordinate gradients (2011, methodology): “When the SVM hinge loss is used, the target function is known to be the Bayes rule [18, 37] which is usually not continuous.”
Altitude Training: Strong Bounds for Single-Layer Dropout (2014, methodology): “Our goal is to train a weight vector w that classiﬁes new examples with features x via a linear decision rule We start with the usual empirical risk minimizer: b for some loss function ` (we will analyze the zero-one loss but use logistic loss in experiments [e.g., 10, 14, 15]).”
The Tradeoffs of Large Scale Learning (2007, background): “This tradeoff has been extensively discussed in the literature [2, 3] and lead to excess error that scale between the inverse and the inverse square root of the number of examples [7, 8].”